Typically, a global positioning system (GPS) can provide a user with a position, velocity, and time (PVT) solution, sometimes referred to as a navigation solution. The global positioning system includes a GPS receiver which typically incorporates current measurements from four or more GPS satellites to update its most recent PVT solution using some navigation algorithm. Pseudorange measurements can be referred to as the range or distance between a satellite and the GPS receiver. To determine a receiver position, the GPS receiver typically determines the ranges to at least three satellites as well as their positions at the time of transmitting. The satellites positions can be calculated for any point in time with known satellite orbital parameters, which are broadcast by the satellites.
The pseudorange measurements can be computed using measured time of signal transmission from the satellite to the GPS receiver, multiplied by the speed of light. Pseudorange measurements are called “pseudo” since the internal clock time of the receiver and GPS time are normally unsynchronized resulting in an unknown, such as, the receiver clock offset Δt, among others, that is typically computed by the navigation algorithm. Thus, with at least four signals, solutions for the receiver position along the x-, y-, z- and Δt-axes can be computed.
To achieve accuracy and integrity, the GPS receiver typically includes algorithms that contain some failure detection and exclusion (FDE) functions to detect and exclude failed pseudorange measurements. GPS measurements can be affected by multipath signals, where the GPS signals reflect off, for example, surrounding terrain, buildings, canyon walls, and hard ground, among others. When a signal is reflected, the signal typically passes through a longer path than the corresponding direct-path signal. Thus, the multipath signal can affect the pseudorange measurements, resulting in potential unexpected errors. Accordingly, pseudorange residuals, also known as, innovations or errors, can be referred to as a pseudorange measurement minus an estimated range. Many FDE functions can determine whether the pseudorange measurements are normal or failures based typically on the magnitude of the pseudorange residuals. It should be noted that since one pseudorange measurement typically corresponds to a pseudorange residual, these two terms sometimes can be exchanged. For example, processing pseudorange measurement residual has the same meaning as processing pseudorange measurement. The two terms will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description.
A large pseudorange residual typically indicates a failure or a potential failure. The FDE function can either exclude or de-weight the failed measurements in the navigation computation. However, the FDE algorithms have a certain probability of false alarms, such as, for example, mistakenly excluding good measurements, and a certain probability of misdetections, such as, for example, failing to detect bad measurements. Excluding measurements can adversely affect satellite geometry distribution or, in other words, dilution of position (DOP), which, in turn, can magnify measurement errors into position solution errors. In addition, excluding a pseudorange measurement among only three or four available pseudorange measurements can reduce GPS availability.
De-weighing a pseudorange measurement is often achieved by supposing that the error distribution is a zero-mean Gaussian and then by inflating its error variance. Unfortunately, the de-weighing mechanism has some deficiencies for utilizing failed measurements. For example, multipath error is usually not zero-mean; thus, simply inflating the error variance of a zero-mean Gaussian does not correctly reflect its actual error characteristics. In another example, received multipath signals can last longer when the GPS receiver is stationary or slowly moving than when the GPS receiver is fast moving. Any improper mitigation of a multipath effect can potentially cause the position fix to drift away after a certain amount of time when the GPS receiver is stationary or slowly moving.